The spectrum for large sets of disjoint mendelsohn triple systems with any index

The spectrum for LMTS(v,1) has been obtained by Kang and Lei (Bulletin of the ICA, 1993). In this article, firstly, we give the spectrum for LMTS(v,3). Furthermore, by the existence of LMTS(v,1) and LMTS(v,3), the spectrum for LMTS(v,λ) is completed, that is v ≡ 2 (mod λ), v ≥ λ + 2, if λ ? 0(mod 3) then v ? 2 (mod 3) and if λ = 1 then v ≠ 6. © 1994 John Wiley & Sons, Inc.